# Algebra Puzzle – Challenge 35

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## Challenge:

The ratio of the ages of Eric and Tara is 2 to 3 and the ratio of the ages of Tara and Marshall is 9 to 7. If the sum of their ages is 66, then how old is Eric?

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Let E be the age of Eric, T be the age of Tara and M be the age of Marshall.
E + T + M = 66
The ratio of E to T is 2 to 3. So:
$$E = \frac{2}{3} T$$
The ratio of T to M is 9 to 7. So:
$$M = \frac{7}{9} T$$
Replace the value of E and M in the first equation with their values in the second and third equations:
$$\frac{2}{3} T + T + \frac{7}{9} T = 66 → \frac{22}{9} T = 66 → T = 27$$
$$E = \frac{2}{3} T ⇒ E = \frac{2}{3} (27) = 18$$
Eric is 18 years old now.

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